How can I create a new object in the Outliner?
You have to be careful in witch mode you add a new object. If you are in object mode you add the new mesh as its own object and you can see it in the outliner as its own item with its own modifiers, etc. but if you are in edit mode inside another object and you add the new mesh in edit mode it becomes part of the geometry of the object you are in edit mode of sharing that objects texture, modifiers, etc.